Answer:
$450
Explanation:
The interest of the loan can be calculated using the following equation:
[tex]I=P\cdot r\cdot t[/tex]Where P is the amount that he borrowed, r is the interest rate and t is the number of years.
So, replacing P by 2500, r by 0.06, and t by 3 years, we get:
[tex]\begin{gathered} I=2500^{}\cdot0.06\cdot3 \\ I=450 \end{gathered}[/tex]Then, the interest of the loan is $450.
There are 152 students at a small school and 45 of them are freshmen. What fraction of the students are freshmen? Use "/" for the
fraction bar. Do not use spaces in your answer.
45/152 is fraction of the students are freshmen.
What are fraction?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction is a portion of a whole and is used to represent how many pieces of a particular size there are while speaking in ordinary English, for example, one-half, eight-fifths, and three-quarters. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. There is a proportion there in numerator or denominator of a complicated fraction. There are three main categories of fractions in mathematics. Proper fractions, incorrect fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions.
Total students = 152
Freshman = 45
Fraction = 45/152
This is the simplest form .
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A company purchased 10,000 pairs of men'sslacks for $18.66 per pair and marked them up $22.93. What was the selling price of each pair of slacks? Use the formulaS=CMThe selling price of each pairs of slacks is ?
Given:
A company purchased slacks for $18.66 per pair.
Mark up= $22.93
[tex]\begin{gathered} \text{Selling price= cost price +mark up} \\ \text{Selling price=}18.66+22.93 \\ \text{Selling price= \$41.59} \end{gathered}[/tex]Factor completely: 3x'2 + 6x + 3a. (3x + 1) (x + 6)b. (3x + 3) (x + 1)c. 3(x + 1)'2d. 3(x + 1) (x-1)the 2s with the commas are exponents
3x^2 + 6x + 3
a= 3
b= 6
c = 3
Find the product of a and c
3x3 = 9
Now, find a product that equal 3x3 and equals be when added
b= 6
3+3 = 6
3x3= 9
Rewrite the expression with the new numbers taking the middle place:
3x^2 +3 x+ 3x +3
Isolate terms and factor out the greatest common factor:
(3x^2 +3 x) + (3x +3)
3x ( x+1) + 3 (x+1)
Factor out x+1 and rewrite:
(3x+3) (x+1)
In 2011 Staci invested $13,000 in a savings account for her newborn son. The account pays 3.6% interest each year. Determine the accrued value of the account in the year 2029, when her son will go to college. Round your answer the nearest cent.In the year 2029, the accrued value will be $
To solve this problem, we can use the compound interest formula
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where A represents the accrued value, P represents the invested value, r represents the interest(in decimals), n represents the amount of times the interest is compounded per unit 't' and t represents the time.
Since the unit of the time 't' is years, and the interest is compounded yearly, n = 1.
To write a percentage as a decimal, we just have to divide the percentage value by 100.
[tex]3.6\%=0.036[/tex]To find the amount of time t, we just have to subtract the year the money was invested from the year we want to know the money accrued.
[tex]t=2029-2011=18[/tex]Then, using those values on the formula, we have
[tex]\begin{gathered} A=13,000(1+0.036)^6 \\ A=16073.1828298\ldots\approx16073.18 \end{gathered}[/tex]The accrued value in the year 2029 will be $16,073.18.
Samantha drinks 2/3 gallon of water everyday.At this rate , how much water does Samantha drink in 30 days ?
Explanation:
We are told that Samantha drinks 2/3 gallon of water daily
We are then asked to find the volume of water that she will drink in 30 days
To do so, we will have:
[tex]\begin{gathered} if\text{ } \\ \frac{2}{3}gallons\text{ =1 day} \\ for\text{ } \\ 30\text{ days, this will be} \\ \frac{2}{3}gallons\text{ per day}\times30days\text{ =}\frac{60}{3}=20gallons \end{gathered}[/tex]Therefore, in 30 days, she will drink 20 gallons of water
The answer is 20 gallonsans
Find the midpoint of the segment below and enter its coordinates as anordered pair. If necessary, express coordinates as fractions, using the slashmark ( 1 ) for the fraction bar.
Consider that the coordinates of the mid-point of a line segment is given by the formula,
[tex]\begin{gathered} x=\frac{x_1+x_2}{2} \\ y=\frac{y_1+y_2}{2} \end{gathered}[/tex]The given diagram represents the line segment between the points (-3,4) and (-6,-1).
So the corresponding mid-point is given by,
[tex]\begin{gathered} x=\frac{-3+(-6)}{2}=\frac{-9}{2} \\ y=\frac{4+(-1)}{2}=\frac{3}{2} \end{gathered}[/tex]Thus, the mid-point of the given line segment is ( -9/2 , 3/2 ) .
What is the measure of ?ХvO A. 46°42°42"38°NуvO B. 42°O C. 40°O D. 38°
The value Z is denoted as the center of the circle. Therefore, arc UV and arc XY should be the same .
[tex]undefined[/tex]Answer: A. 42°
Step-by-step explanation:
Hope this helps :)
Last year, Susan had $20,000 to invest. She invested some of it in an account that paid 10% simple interest per year, and she invested the rest in an account that paid 7% simple interest per year. After one year, she received a total of $1790 in interest. How much did she invest in each account?
Last year, Susan had $20,000 to invest. She invested some of it in an account that paid 10% simple interest per year, and she invested the rest in an account that paid 7% simple interest per year. After one year, she received a total of $1790 in interest. How much did she invest in each account?
Let
x ------> amount invested in an account that paid 10% simple interest per year
20,000-x ------> amount invested in an account that paid 7% simple interest per year
so
The formula of simple interest is equal to
I=P(rt)
In this problem we have that
10%=0.10
7%=0.07
x*(0.1)+(20,000-x)*(0.07)=1,790
solve for x
0.10x+1,400-0.07x=1,790
0.03x=1,790-1,400
0.03x=390
x=$13,000
therefore
amount invested in an account that paid 10% simple interest per year was $13,000and amount invested in an account that paid 7% simple interest per year was $7,000Vera cut a piece of fabric into 5 equal-length pieces. Then she cut another 3 centimeters off one piece, leaving 6 centimeters of fabric. How many centimeters long was her original piece of fabric? Write two equations with letters for the unknowns. Solve.
We have
fabric cut into 5 equal -length pieces
she cut 3 cm
l=length of one piece of the 5 equals pieces
l=6+3
l=9
the original piece of fabric is
o= length of the original fabric
o=5l
o=5(9)
o=45 cm
the original piece of fabric is 45 cm
A disk is in the form of square and measures 5.25inches on each side. Find the diagonal length of thedisk. I am taking geometry In the 8th grade and I am lost
Answer:
The diagonal length is 7.42 inches.
Explanation:
The disk with its diagonal is:
Then, we can look at the diagonal as the hypotenuse of a right triangle. Then, if we call D to the diagonal:
[tex]\begin{gathered} D^2=(5.25in)^2+(5.25)^2 \\ D=\sqrt{2(5.25in)^2}\approx7.42in \end{gathered}[/tex]cabrinha run 3/10 mile each day for 6 days how many miles did she run in off
3/10 mile per day for 6 days.
To find how many miles did she run multiply the miles per day by 6days:
[tex]\frac{3\text{mile}}{10\text{day}}\cdot6\text{days}=\frac{18}{10}\text{mile}=\frac{9}{5}\text{mile}[/tex]Then, in 6 days she run 9/5 mileIf your distance from the foot of the tower is 20 m and the angle of elevation is 40°, find the height of thetower.
We have to use the tangent of angle 40 to find the height of the tower.
[tex]\text{tan(angle) = }\frac{opposite\text{ side}}{\text{adjacent side}}[/tex]The adjacent side is 20m, and the angle is 40 degrees, then
[tex]\tan (40)\text{ = }\frac{height\text{ of the tower}}{20m}[/tex][tex]\text{height = 20m }\cdot\text{ tan(40) = 20m }\cdot0.84\text{ = }16.8m[/tex]Therefore, the height of the tower is 16.8m
giving the figure below, what is the measure of angle JKL
The measure of < JKL = 25+25 = 50 degrees.
Angle JOK = 360 -230 = 130 degrees , (where O is the center of the circle)
< OLK = < OJK = 90 degrees ( tangent to a circle)
< LOK = < JOK = 180 - (90+65) = 180 - 155 = 25 degrees
The solution is: < JKL = 25 +25 = 50 degrees
(3x10⁴) (2x10⁵)Find the answer by simplifying
The given expression (3x10⁴) (2x10⁵)
we seperate the terms and collect like terms:
[tex]\begin{gathered} \mleft(3\times10^{4}\mright)(2\times10^{5})\text{ = 3}\times10^{4}\times2\times10^{5} \\ =\text{ 3}\times2\times10^{4}\times10^{5} \end{gathered}[/tex]When multiplying exponent (power) of the same base, the exponenet of the two numbers (base) are added together.
[tex]\begin{gathered} \text{Base = 10 , exponent = 4 and 5} \\ =3\times2\times10^{4+5} \\ =\text{ 6}\times10^9 \end{gathered}[/tex]
Polynomial Functions:Find P(-1) and p(2) for each function.“P(x) = 4-3x”
P(-1):
[tex]\begin{gathered} P(-1)=4-3(-1) \\ P(-1)=4+3 \\ P(x)=7 \end{gathered}[/tex]P(2):
[tex]\begin{gathered} P(2)=4-3(2) \\ P(2)=4-6 \\ P(2)=-2 \end{gathered}[/tex]Earth's Moon is 384,400 km from Earth. What is the correct way to write this distance in scientific notation? O A. 3.844 x 105 km OB. 38.44 x 10-4 km O C. 38.44 x 104 km O D. 3.844 x 10-5 km SUBMIT
To do this, move the decimal in such a way that there is a non-zero digit to the left of the decimal point. The number of decimal places you shift will be the exponent by 10. If the decimal is shifted to the right the exponent will be negative. If the decimal is shifted to the left, the exponent will be positive.
So, in this case, you have
Therefore, the correct way to write this distance in scientific notation is
[tex]3.844\times10^5[/tex]And the correct answer is
[tex]undefined[/tex]A father is buying cheeseburgers for his children. Each cheeseburgercosts $3.50. He spends $17.50 on cheeseburgers. Which equation canyou use to determine how many cheeseburgers he bought?O 17.50 = 3.50cO 3.50 = 17.500O 3.50 + 17.50 =cO 17.50 -3.50 = C« PreviousNext
Each cheese burger costs $3.50
c reprsents the number of cheese burgers
$17.50 is the total cost spent on c cheeseburgers
If you multiply the value of each cheeseburger by the number bought, you'll obtain the total cost:
3.50c=17.50
The correct option is number 1
Simplify (sqrt)98m^12Using factor tree. Please draw. Quick answer = amazing review. Not a graded or timed assessment. Please use factor tree or split up using perfect squares
The simplified expression is 7m⁶ √2
STEP - BY - STEP EXPLANATION
What to find?
Simplify the given expression.
Given:
[tex]\sqrt[]{98m^{12}}[/tex]To simplify the above, we will follow the steps below:
Step 1
Apply radical rule:
[tex]\sqrt[]{ab}=\sqrt[]{a}\text{ . }\sqrt[]{b}[/tex]That is;
[tex]\sqrt[]{98m^{12}}=\sqrt[]{98}\times\sqrt[]{m^{12}}[/tex]Step 2
Simplify each value under the square root.
[tex]\sqrt[]{98}=\sqrt[]{49\times2}=\sqrt[]{49}\times\sqrt[]{2}=7\sqrt[]{2}[/tex][tex]\sqrt[]{m^{12}}=(m^{12})^{\frac{1}{2}}=m^{\frac{12}{2}}=m^6[/tex]Therefore, the simplified expression is:
[tex]\sqrt[]{98m^{12}}=7m^6\text{ }\sqrt[]{2}[/tex]. Math and Science During winter months, freshwater fish sense the water getting colder and swim to the bottoms of lakes and rivers to find warmer water. If a fish 7 swims of the depth of a 32-foot deep lake, how many feet down did the fish swim?[tex]51[/tex]
The total depth of the lake is:
[tex]32\text{ ft}[/tex]And we need to find how many feet are 7/8 of the depth.
To find how much is 7/8 out of 32 ft what we do is multiply 32 by 7/8:
[tex]32\times\frac{7}{8}[/tex]This multiplication can also be represented as follows:
[tex]\frac{32}{8}\times7[/tex]We start by solving the division:
[tex]4\times7[/tex]and finally, we solve the multiplication:
[tex]4\times7=28[/tex]-->the fish swam 28 ft.
Answer: 28 ft
Figure 1 and Figure Il are similar figures. Figure I Figure II R S А B F C w T E D V U Which proportion must be true?
From the diagram,
CD is corresponding to WR
VW is corresponding to BC
RS is corresponding to DE
ST is corresponding to EF
TU is corresponding to FA
Final answer
[tex]\frac{ST}{EF}\text{ = }\frac{WR}{CD}[/tex]Find the side length of a cube with a volume of 111 ft³ If necessary, round your answer to the nearest tenth.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
volume of a cube
V = 111 ft³
side lenght = ?
Step 02:
volume of a cube
V = s³
[tex]\begin{gathered} 111ft^{3\text{ }}=\text{ s } \\ \sqrt[3]{111ft^3}\text{ = s } \end{gathered}[/tex]4.81 ft ³ = s
The answer is:
The side length is 4.8 ft³
Carmen has 12 loaves of pumpkin bread. She cuts each loaf into 1/8 pieces and gives one piece to each of her friends. How many friends can Carmen give a piece of pumpkin bread?
12 loaves of pumpkin bread.
Each loave is cut into 1/8 pieces.
So, there are 8 pieces per loaf:
8 pieces per loaf x 12 loaves = 96 pieces
If she gives one piece to each friend she can give it to 96 friends:
96 pieces / x friends = 1 per friend
96/x =1
96 = x(1)
96= x
Match the following. Match the items in the left column to the items in the right column.1. divisor2. decimal fraction3. algorithm4. fraction5.quotient6. reminder7. doidonsa. the result of dividing two numbersb. the number being dividedc. a set of rules to be followed tosolve a problemd. the number of equal parts a number is being divided intoe. a fraction in which the denominator is 10 or a power of 10f. the amount left over after Chivisiong. a number that expresses the portiona whole
We can match as follows:
1. divisor ----> d. the number of equal parts a number is being divided into
2. decimal fraction ----> e. a fraction in which the denominator is 10 or a power of 10
3. algorithm ----> c. a set of rules to be followed to solve a problem
4. fraction ----> g. a number that expresses the portion
5. quotient ----> a. the result of dividing two numbers
6. reminder ----> f. the amount left over after Division
Picture explains it all
Evaluate the indicated function for f(x)=x^2-1 & g(x)=x-2 algebraically .
Given:
[tex]f(x)=x^2-1\text{ ; g(x)=x-2 }[/tex][tex](\frac{f}{g})(t+2)=\frac{f(t+2)}{g(t+2)}[/tex][tex](\frac{f}{g})(t+2)=\frac{(t+2)^2-1}{(t+2)^{}-2}[/tex][tex](\frac{f}{g})(t+2)=\frac{t^2+4t+4-1}{t+2-2}[/tex][tex](\frac{f}{g})(t+2)=\frac{t^2+4t+3}{t}[/tex][tex](\frac{f}{g})(t+2)=\frac{(t+1)(t+3)}{t}[/tex]Sarina throws a ball up into the air, and it falls on the ground nearby. The ball's height, in feet, is modeled by the function ƒ(x) = –x2 – x + 3, where x represents time in seconds. What's the height of the ball when Sarina throws it?Question 12 options:A) 1 footB) 3 feetC) 4 feetD) 2 feet
Answer:
3 feet
Explanation:
We are told from the question that the ball's height, in feet, is modeled by the below function;
[tex]f(x)=-x^2-x+3[/tex]where x = time in seconds
To determine the height of the ball when Sarina throws the ball, all we need to do is solve for the initial height of the ball, i.e, the height when x = 0. So we'll have;
[tex]\begin{gathered} f(0)=-(0)^2-(0)+3 \\ f(0)=3\text{ f}eet \end{gathered}[/tex]Part A: The Sun that produces 3.9 * 10^33ergs of a radiant energy per second. How many eggs of radiant energy does the Sun produce and 3.25 * 10^3 seconds?Part B: Which is more the reasonable measurement of the distance between the tracks on a railroad: 1.435 * 10^3mm or 1.435 * 10^3mm?
Part A
[tex]1.2675\times10^{37}ergs[/tex]Explanations:The sun can produce 3.9 * 10^33 ergs of radiant energy per second
[tex]\text{Amount of energy in 1 second = 3.9 }\times10^{33}ergs[/tex][tex]\text{Amount of energy produced in 3.25}\times10^3\sec \text{ = (3.9}\times10^{33}\times3.25\times10^3)[/tex][tex]\text{Amount of energy produced in 3.25}\times10^3\text{ seconds = }1.2675\times10^{37}ergs[/tex]I don't understand any of this (for a practice assessment)
Answer:
a. The total weight
b. 2 times the weight of Jet
c. The weight of Fido
d. The total weight
Explanation:
We know that Fido weighs 10 pounds more than Jet and together they weigh 46 pounds. So, if j represents Jet's weight, the bar model is:
Now, we can answer each part as:
a. 46 represents the total weight of the small dogs
b. 2j represents 2 times the weight of Jet
c. j + 10 represents the weight of Fido because its weight is the weight of Jet j added to 10.
d. 2j + 10 also represents the sum of the weights of the small dogs.
So, the answers are:
a. The total weight
b. 2 times the weight of Jet
c. The weight of Fido
d. The total weight
I have question 3 and need to know a b and c
a) Recall that:
[tex]-1\le\cos \theta\le1.[/tex]Therefore:
[tex]\begin{gathered} -1\le\cos (30^{\circ}\times t)\le1, \\ -12\le12\cos (30^{\circ}\times t)\le12, \\ -12+16\le12\cos (30^{\circ}\times t)+16\le12+16, \\ 4\le12\cos (30^{\circ}\times t)+16\le28. \end{gathered}[/tex]Therefore the minimum height of the Ferris wheel above the ground is 4 meters.
b) Recall that to evaluate a function at a given value, we substitute the variable by the given value, then, evaluating the given function at t=3 we get:
[tex]12\cos (30^{\circ}\times3)+16.[/tex]Simplifying the above result we get:
[tex]\begin{gathered} 12\cos (90^{\circ})+16, \\ 12\cdot0+16, \\ 0+16, \\ 16. \end{gathered}[/tex]Therefore, the height of the Ferris wheel above the ground after 3 minutes is 16 meters.
(c) Let x be the time in minutes the Ferris wheel takes to complete one full rotation, then we can set the following equation:
[tex]30^{\circ}\times x=360^{\circ}.[/tex]Therefore:
[tex]30x=360.[/tex]Dividing the above equation by 30 we get:
[tex]\begin{gathered} \frac{30x}{30}=\frac{360}{30}, \\ x=12. \end{gathered}[/tex]Answer:
(a) 4 meters.
(b) 16 meters.
(c) 12 minutes.
Two methods to solve (X+3)^2=6
The solution of the given equation is [tex]-3+\sqrt{6}[/tex] and [tex]-3-\sqrt{6}[/tex].
Given equation:-
[tex](x+3)^2=6[/tex]
We have to find the value of x by solving the given equation.
We can rewrite the given equation as:-
[tex]x^2+6x+9=6\\x^2+6x+3=0[/tex]
We can solve the the quadratic equation by finding the discriminant.
[tex]x = \frac{-6+-\sqrt{6^2-4*1*3} }{2*1}[/tex]
[tex]x = \frac{-6+-\sqrt{36-12} }{2}[/tex]
[tex]x=\frac{-6+-2\sqrt{6} }{2}=-3+-\sqrt{6}[/tex]
Hence, the values of x are [tex]-3+\sqrt{6}[/tex] and [tex]-3-\sqrt{6}[/tex].
Discriminant
In arithmetic, a polynomial's discriminant is a function of the polynomial's coefficients.
Quadratic equation
The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics. It is expressed in the form of:
ax² + bx + c = 0
where x is the unknown variable and a, b and c are the constant terms.
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